A zero coupon bond is a contract where one party offers a fixed payment at a pre-specified

time point which is called its maturity. A forward rate curve is a theoretical function that encodes the

prices of all possible bonds with varying maturities at one given point of time. There are various models

that explain the behaviour of forward rate curves accross time. The most principle model in this direction

is the Heath Jarrow Morton (HJM)-model which models the forward rate curve directly. This model is

known to be free of arbitrage if and only if the HJM-drift condition holds.

We are interested in finite dimensional HJM-models which stay on one fixed given finite dimensional

manifold, roughly spoken this means that the model stays within a fixed finitely parametrised family

of curves. It is well known, that a curve valued process can only stay on a prescribed manifold if the

Stratonovich drift is tangential to the manifold at all time, or more simply, if we can instead find a

parameter process which selects the curve seen at a given time. From a statistical point of view it would

be desirable to leave the diffusion coefficient of the parameter process open for estimation, or in the

language of manifolds that means that any tangential diffusion coefficient should be left open as possible.

In this presentation, we find those finite dimensional manifolds where the diffusion coefficient remains

fully open for estimation while still allowing for the HJM-drift condition to be met. It turns out that the

resulting manifolds are nowhere locally affine. More so, they are nowhere affinely foliated as has been

suggested by earlier work (however under different assumptions).